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  1. See, for example, A. Yariv, Optical Electronics (Holt, Rinehart, & Winston, New York, 1976).
  2. See, for example, J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).
  3. Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
    [CrossRef]

1986 (1)

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Alfano, R.

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Gaskill, J. D.

See, for example, J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).

Ho, P.

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Manassah, J. T.

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Mustafa, M.

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Yariv, A.

See, for example, A. Yariv, Optical Electronics (Holt, Rinehart, & Winston, New York, 1976).

IEEE J. Quantum Electron. (1)

Large chirping for ultrafast pulses can occur as a result of self-phase modulation or induced phase modulation. See J. T. Manassah, M. Mustafa, R. Alfano, P. Ho, “Spectral Extent and Pulse Shape of the Supercontinuum for Ultrashort Laser Pulse,” IEEE J. Quantum Electron. QE-22, 197 (1986);“Induced Supercontinuum and Steepening of an Ultrafast Laser Pulse,” Phys. Lett. A 113, 242 (1985).
[CrossRef]

Other (2)

See, for example, A. Yariv, Optical Electronics (Holt, Rinehart, & Winston, New York, 1976).

See, for example, J. D. Gaskill, Linear Systems, Fourier Transforms and Optics (Wiley, New York, 1978).

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Equations (18)

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H ( ω ) = exp { [ ( ω ω f ) / 2 Δ ] 2 } ,
out ( ω ) = H ( ω ) in ( ω ) .
E in ( t ) = exp ( i ω 0 t ) A ( t ) exp [ i ϕ ( t ) ] ,
E out ( t ) = Δ π exp ( i ω f t ) d t A ( t ) exp [ i ϕ ( t ) ] × exp [ i ( ω 0 ω f ) t ] × exp [ ( t t ) 2 Δ 2 ] ,
A ( t ) = exp ( t 2 τ 2 ) ,
ϕ ( t ) = b 2 t 2 ,
E out ( t ) = Δ ( Δ 2 + τ 2 ) 1 / 2 exp ( i ω f t ) exp [ t 2 ( Δ 2 τ 2 ) Δ 2 + τ 2 ] ,
τ eff = ( Δ 2 + τ 2 ) τ 2 Δ 2
τ eff = τ ,
τ eff = Δ 1 ,
E out ( t ) = Δ [ Δ 2 + τ 2 + i b 2 ] 1 / 2 exp ( i ω f t ) × exp ( i b eff 2 t 2 ) exp ( t 2 τ eff 2 ) ,
b eff 2 = b 2 Δ 4 ( Δ 2 + τ 2 ) 2 + b 4 ,
τ eff 2 = Δ 2 Δ 4 ( Δ 2 + τ 2 ) ( Δ 2 + τ 2 ) 2 + b 4 .
( i ) b Δ and b τ 1 then τ eff = Δ 1 and b eff 0 ;
( ii ) Δ b τ 1 then τ eff = Δ b 2 and b eff b ;
Δ b and τ 1 b
then τ eff = τ if Δ τ 1 ,
τ eff = Δ 1 if Δ τ 1 .

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